Molecular computing executed via local interactions of spatially contiguous
set of molecules has potential advantages of (i) speed due to increased local
concentration of reacting species, (ii) sharper switching behavior due to single
molecule interactions, (iii) parallelism since each circuit operates
independently of another and (iv) modularity and scalability due to the ability
to reuse DNA sequences in spatially separated regions. We propose detailed
designs for local molecular computations that involve spatially contiguous
molecules arranged on addressable substrates. The circuit acts via enzyme-free
DNA hybridization reaction cascades. Our designs include composable OR, AND,
propagation Boolean gates and techniques to achieve higher degree fan-in and
fan-out. A biophysical model of localized hybridization reactions is used to
estimate the effect of locality on reaction rates. We also use the Visual DSD
simulation software in conjunction with these localized reaction rates to
simulate a localized circuit for computing the square root of a four bit
number.